Optical parametric oscillator and second harmonic generator using monoclinic phase Ga2S3 crystal

ABSTRACT

This disclosure provides a second harmonic generator and an optical parametric oscillator, the second harmonic generator and the optical parametric oscillator comprise one or more nonlinear optical frequency conversion crystal and a pump laser source, the nonlinear optical frequency conversion crystal is a monoclinic Ga.sub.2S.sub.3 crystal, the space group of the monoclinic Ga.sub.2S.sub.3 crystal is Cc, and the unit cell parameters are a=11.1.ANG., b=6.4.ANG., c=7.0.ANG., .alpha.=90.degree., .beta.=121.degree., .gamma.=90.degree., and Z=4.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a Continuation Application of InternationalApplication No. PCT/CN2012/086248, filed Dec. 10, 2012, which claimspriority to Chinese Patent Application No. 201210190280.8, filed Jun.11, 2012, and Chinese Patent Application No. 201210190288.6, filed Jun.11, 2012, the entire disclosures of which are incorporated herein byreference in their entireties.

TECHNICAL FIELD

This disclosure relates to an optical parametric oscillator and a secondharmonic generator using a monoclinic phase Ga₂S₃ crystal as infraredband second order nonlinear optical materials.

BACKGROUND

Optical parametric oscillators and second harmonic generators arecommonly used nonlinear optical devices, and the second order nonlinearoptical material is the key material for achieving the function thereof.For a second order nonlinear optical material in the infrared region,this disclosure uses a monoclinic phase Ga₂S₃ crystal which has neverbeen used in the art, obtaining an optical parametric oscillator and asecond harmonic generator having high laser damage threshold.

Because of the application of laser technology, the nonlinear opticalcrystal materials have drawn increasing attention of the public. Inparticular, the second order nonlinear optical crystal materials of deepultraviolet and middle/far infrared regions, which are far fromsatisfying the requirements of the applications due to the lack ofvarieties, have become the hot spot of research. The chalcogenide systemhas become a direction of the research of middle/far infrared secondorder nonlinear optical crystal, wherein, for example, AgGaS₂ (AGS),AgGaSe₂ (AGSe), AgGa_((1-x))In_(x)Se₂, GaSe, LiInS₂ (LIS), LiInSe₂, andthe like have drawn wide attention. These chalcogenides are mainlyternary compounds or more. Less attention is paid to the research of thesecond order nonlinear optical properties of binary chalcogenidecompounds. However, comparing with the ternary compounds or more, thebinary chalcogenides generally have the advantages of simple structure,convenient synthesis, stable physical and chemical features, and so on.

Ga₂S₃ has three crystal phases: monoclinic phase (Cc), hexagonal phase(P6₃mc) and cubic phase (F-43m), which are all noncentrosymmetric spacegroups, meaning that Ga₂S₃ may have second order nonlinear opticaleffects. In 1961, Goodyear et al. reported the monoclinic phasestructure (Cc) of Ga₂S₃ in Acta Crystal for the first time. There is noreport regarding using Ga₂S₃ as the infrared second order nonlinearoptical materials hitherto.

There are two known synthetic methods for Ga₂S₃, both of which employ Gaand S elementary materials as the starting reactants. The first methodcomprises mixing Ga and S in a proper ratio, enclosing into a evacuatedquartz tube, keeping at 450° C. for 5 days, and then heating at a rateof 50° C./12 h to a temperature of 1100° C., and naturally cooling downto obtain polycrystalline powders of Ga₂S₃. The second method comprisesplacing equal amount of Ga and S into two quartz boats in a flame-sealedquartz tube under a vacuum condition, heating the quartz boat containingGa to 1150° C., and heating the quartz boat containing S to 450-500° C.After one day, polycrystalline powders of Ga₂S₃ are formed on one end ofthe quartz boat containing Ga. The Ga₂S₃ obtained in both methods are ofa monoclinic phase. Embodiments of the disclosure use Ga₂O₃, S powder,and B powder as the starting materials, and synthesize monoclinic phaseGa₂S₃ employing a high temperature solid-state boron-sulfur method.

SUMMARY

In some embodiments of the disclosure, it is provided a second harmonicgenerator, comprising one or more nonlinear optical frequencyconversioncrystal and a pump laser source, wherein the nonlinear opticalfrequency conversioncrystal is a monoclinic Ga₂S₃ crystal, the spacegroup of the monoclinic Ga₂S₃ crystal is Cc, and the unit cellparameters are a=11.1 Å, b=6.4 Å, c=7.0 Å, α=90°, β=121°, γ=90°, andZ=4.

In some embodiments of the disclosure, it is provided an opticalparametric oscillator, comprising, in the light path, a first lens, alaser crystal, a second lens, a nonlinear optical crystal, and thirdlens in this order, wherein an optical parametric oscillation chamber isformed between the second lens and the third lens, and the nonlinearoptical crystal is a monoclinic Ga₂S₃ crystal, the space group of themonoclinic Ga₂S₃ crystal being Cc, and the unit cell parameters beinga=11.1 Å, b=6.4 Å, c=7.0 Å, α=90°, β=121°, γ=90°, and Z=4.

DESCRIPTION OF FIGURES

FIG. 1 is the powder X-ray diffraction pattern of a compound of oneembodiment of this disclosure.

FIG. 2 is the infrared absorption spectrum of a compound of oneembodiment of this disclosure.

FIG. 3 is the UV-Vis diffuse reflectance spectroscopy of a compound ofone embodiment of this disclosure.

FIG. 4 the phase matching pattern at 1910 nm of a compound of oneembodiment of this disclosure.

SPECIFIC EMBODIMENTS

In some embodiments disclosed in the disclosure, the pump laser sourceincludes a liquid laser, a solid laser, a gas laser or a semiconductorlaser.

In some embodiments disclosed in the disclosure, the wavelength of thelaser emitted by the pump laser source is in a range of from 1 to 20micrometers.

In some embodiments disclosed in the disclosure, the pump laser sourceincludes a continuous wave laser, or a pulse laser.

In some embodiments disclosed in the disclosure, manners for achievingphase matching in the nonlinear optical crystal by the pump laser sourcecomprise collinear, non-collinear, critical and non-critical phasematching.

In some embodiments disclosed in the disclosure, the area of themonoclinic Ga₂S₃ crystal is from 0.5 to 5 cm².

In some embodiments disclosed in the disclosure, the area of themonoclinic Ga₂S₃ crystal is from 1.0 to 5 cm².

In some embodiments disclosed in the disclosure, the area of themonoclinic Ga₂S₃ crystal is from 1.5 to 5 cm².

In some embodiments disclosed in the disclosure, the area of themonoclinic Ga₂S₃ crystal is from 2.0 to 5 cm².

In some embodiments disclosed in the disclosure, the area of themonoclinic Ga₂S₃ crystal is from 2.5 to 5 cm².

In some embodiments disclosed in the disclosure, the area of themonoclinic Ga₂S₃ crystal is from 3.0 to 5 cm².

In some embodiments disclosed in the disclosure, the area of themonoclinic Ga₂S₃ crystal is from 3.5 to 5 cm².

In some embodiments disclosed in the disclosure, the area of themonoclinic Ga₂S₃ crystal is from 5 to 10 cm².

In some embodiments disclosed in the disclosure, the output power of thesecond harmonic generator is 0.5 W or more.

In some embodiments disclosed in the disclosure, the output power of theoptical parametric oscillator is 0.5 W or more.

In some embodiments disclosed in the disclosure, it is provided amonoclinic Ga₂S₃ crystal material, and the preparation method thereof.The preparation method is simple and easy to be handled. The materialsources are abundant. The yield of the compound is high. The purity ishigh and the reproductively is good. The preparation method is thereforesuitable for mass production.

In some embodiments disclosed in the disclosure, not only the synthesistemperature (950° C.) is reduced, but also the complicated procedure ofthe traditional operation are avoided, and moreover, the cost is reducedbecause Ga₂O₃ with much lower price is used for replacing Ga.

In some specific embodiments disclosed in the disclosure, the disclosurecomprises the following technical solutions:

A preparation method of a binary metal sulfide crystal material, whereinthe metal sulfide is one of a chemical formula of Ga₂S₃, a monocliniccrystal system, and a Cc space group, and the unit cell parameters area=11.1 Å, b=6.4 Å, c=7.0 Å, α=90°, β=121°, γ=90°, Z=4, wherein Ga₂O₃, B,and S are mixed and grinded at a proper ratio, loaded into a evacuatedand flame-sealed quartz tube, and then treated at a certain temperatureto obtain the monoclinic Ga₂S₃ product.

In some specific embodiments disclosed in the disclosure, the metalsulfide has a three dimensional network frame structure.

In some specific embodiments disclosed in the disclosure, the method isa high temperature solid-state boron-sulfur process for producingmonoclinic phase Ga₂S₃.

In some specific embodiments disclosed in the disclosure, the molarratio of the Ga₂O₃, B, and S is 1:2:3.

In some specific embodiments disclosed in the disclosure, the molarratio of the Ga₂O₃, B, and S is 1:2:3, wherein the amount of S isadditionally 1-3% in excess, preferably 1-2% in excess, to ensure thesufficient reaction.

In some specific embodiments disclosed in the disclosure, the treatmenttemperature is increased at a rate of 30 to 40° C./h to 850-980° C.(preferably 880-950° C., more preferably 900-950° C.), keeping suchtemperature for 48-144 hours (preferably 60-120 h, more preferably60-100 h), and then decreased at a rate of 2 to 6° C./h (preferably 2-5°C./h, more preferably 2-4° C./h) to 250° C.

In some specific embodiments disclosed in the disclosure, thepreparation method comprises mixing and grinding Ga₂O₃, B, and S at amolar ratio of 1:2:3 (preferably, wherein the amount of S isadditionally 1-3% in excess), pressing into pellets and loading into aevacuated quartz tube to be heated, increasing the temperature at a rateof 30 to 40° C./h to 850-980° C. (preferably 880-950° C., morepreferably 900-950° C.), keeping the temperature for 48-144 hours(preferably 60-120 h, more preferably 60-100 h), and then decreasing thetemperature at a rate of 2 to 6° C./h (preferably 2-5° C./h, morepreferably 2-4° C./h) to 250° C., turning off the power source, takingout the quartz tube, and washing away the byproduct B₂O₃ with hot water,to obtain monoclinic phase Ga₂S₃ as pale yellow microcrystal.

In some specific embodiments disclosed in the disclosure, the yield ofthe production method of the disclosure is 90% or more, preferably 95%or more, or 98% or more.

The specific reaction formula of the disclosure is:Ga₂O₃+2 B+3 S→Ga₂S₃+B₂O₃

In some specific embodiments disclosed in the disclosure, the disclosurealso provides the use of the above binary metal chalcogenide monoclinicGa₂S₃ having a three dimensional network frame structure as a nonlinearoptical crystal.

In some specific embodiments disclosed in the disclosure, the use assecond order nonlinear optical materials in the middle/far infraredregions is preferable. More preferably, the monoclinic Ga₂S₃ (preferablyafter it grows into big crystal) is used in the laser applications suchas a second harmonic generator or an optical parametric oscillator, forextending the band range of the laser.

Some specific embodiments disclosed in the disclosure relate to the useof the monoclinic Ga₂S₃ as the second order nonlinear optical materialsin the infrared region, wherein the material has a phase matchingbehavior at 1910 nm, and a powder second harmonic generation (SHG)signal which is 0.7 times of the commercial nonlinear optical crystalKTiOPO₄ (KTP).

Some specific embodiments disclosed in the disclosure relate to the useof the monoclinic phase Ga₂S₃ as second order nonlinear opticalmaterials in the infrared region, wherein, under a 1064 nm laser havinga pulse width of 8 ns, the material has a powder laser damage thresholdof 174 MW/cm². This value is larger than the traditional infrarednonlinear optical crystal AGS (0.03 GW/cm²@1064 nm with τ_(p) as 10 ns)and LIS (0.1 GW/cm²@1064 nm with τ_(p) as 10 ns).

The features of the preparation method of some specific embodiments ofthe disclosure comprise, but not limit to: (1) the source materials areGa₂O₃, S, and B, instead of traditional Ga, S; (2) the ratio betweenmaterials is a special ratio of 1:2:3, with S may be 1-3% slightly inexcess, for ensuring sufficient reaction between the source materials;(3) because heating too fast may burst up the quartz tube, and coolingtoo fast may result in poor quality of crystal and the structuraldisorder, the constant temperature and the duration of the constanttemperature employed in the disclosure determine the crystallizationdegree and the crystal size, such that embodiments of the disclosure mayproduce good nonlinear optical crystal materials.

The disclosure is further described by the following examples. However,the following examples do not limit the disclosure. Any replacement andvariation made to the disclosure are within the scope of the disclosure.

The synthesis of the compound Ga₂S₃ in some embodiments of thedisclosure comprises:

obtaining Ga₂S₃ by a high temperature solid state synthesis method, withthe specific reaction formula being:Ga₂O₃+2 B+3 S→Ga₂S₃+B₂O₃.

The specific operation procedures are:

mixing Ga₂O₃, B, and S according a molar ratio of 1:2:3, pressing intopellets and loading into a evacuated and flame-sealed quartz tube, andthen heating up at a rate of 30˜40° C./h to 850-980° C., keeping thetemperature for 48-144 hours, and then cooling down at a rate of 2-6°C./h to 250° C., finally, turning off the power supply, bringing out thequartz tube, washing away the byproduct B₂O₃ with hot water, to obtainpale yellow block compound microcrystal, with a yield of 90% or more.The single crystal X-ray diffraction measurement and elemental analysistest show that this crystal is a monoclinic phase Ga₂S₃.

Example 1 The Synthesis of 1 mmol Monoclinic Phase Ga₂S₃

1 mmol of Ga₂O₃ (187 mg), 2 mmol of B powder (22 mg), and 3 mmol of Spowder (97 mg, 1% in excess) were weighted, placed into an agate mortarand grinded for about 10 min to be uniformly mixed, and then the mixturewas pressed into a pellet, which was sealed into a quartz tube having alength of about 10 cm, an outer diameter of 13 mm and an inner diameterof 11 mm with oxy-hydrogen flame under a degree of vacuum less than 10Pa. The quartz tube was placed into a muffle furnace, and heated up at arate of 30° C./h to 920° C. The temperature was kept for 60 hours, andthen decreased at a rate of 5° C./h to 250° C. The power supply wasturned off and the temperature was naturally reduced to roomtemperature. The quartz tube was taken out. After the tube was opened,it was washed with hot water to remove byproduct B₂O₃, obtaining about 1mmol of monoclinic phase Ga₂S₃ polycrystalline powder, with a yield of90% or more.

The crystal structure parameters in some embodiments of this disclosureare: a=11.117(9) Å, b=6.406(5) Å, c=7.033(5) Å, α=90°, β=121.15(9)°,γ=90°, Z=4. The crystal structure analysis shows that, this compound hasa simple three dimensional network frame structure, crystallized at anoncentrosymmtric space group Cc.

Example 2 The Synthesis of 30 mmol Monoclinic Phase Ga₂S₃

30 mmol of Ga₂O₃ (5623 mg), 60 mmol of B powder (649 mg), 90 mmol of Spowder (2943 mg, 2% in excess) were weighted, placed in a ball mill andmilled at 400 r/min for 2 h to be uniformly mixed, and then the mixturewas pressed into a pellet, which was sealed into a quartz tube having alength of about 15 cm, an outer diameter of 23 mm and an inner diameterof 20 mm with oxy-hydrogen flame under a degree of vacuum less than 10Pa. The quartz tube was placed into a muffle furnace, and heated up at arate of 30° C./h to 900° C. The temperature was kept for 60 hours, andthen decreased at a rate of 5° C./h to 250° C. The power supply wasturned off and the temperature was naturally reduced to roomtemperature. The quartz tube was taken out. After the tube was opened,it was washed with hot water to remove byproduct B₂O₃, obtaining about30 mmol of monoclinic Ga₂S₃ polycrystalline powder, with a yield of 90%or more.

This example shows that the method may be used for massive synthesismonoclinic Ga₂S₃ polycrystalline powder, which is the basis of thegrowth of monoclinic Ga₂S₃ big crystal in the next step.

Example 3 The Synthesis of Monoclinic Ga₂S₃ Crystal

Monoclinic Ga₂S₃ crystal was grown using the Bridgman-Stockbargermethod. The growth device of crystal was a modified two-zone Bridgmanfurnace. The controlling device was an 808P programmable automatictemperature controller. The source material used was 3 g of Ga₂S₃polycrystalline material synthesized in Example 2.

Specific steps were as following. 3 g of Ga₂ S₃ polycrystalline materialprepared in Example 2 was weighted. After uniformly grinding, thematerial was loaded into a quartz tube crucible having an inner diameterof 15 mm and an outer diameter of 18 mm. After evacuated for 2-6 hours,the inner pressure of the quartz tube crucible is about 0.1 Pa, at thistime, the tube was sealed with oxy-hydrogen flame, and the sealed quartztube was loaded into a quartz tube having an inner diameter of 20 mm andan outer diameter of 23 mm. evacuated for 0.5-2 h, and when the innerpressure was slightly higher than 0.1 Pa, the tube was sealed withoxy-hydrogen flame. The sealed double layer quartz tube was placed intoan upper furnace of a Bridgman furnace. The temperature was slowlyincreased to 700° C., and kept for 10 hours. The temperature was thenincreased to 950° C., and then kept for 10 hours. Finally, thetemperature was increased to 1100° C. to melt the materials, and keptfor 20-80 hours. At this time, the crucible was cooled to roomtemperature at a falling rate of 0.5 mm/h. The furnace was shut down.After the sample was cooled, transparent pale yellow Ga₂S₃ singlecrystal was obtained.

Example 4 Performance Test for the Monoclinic Phase Ga₂S₃ Powder

Powder X-ray diffraction test employed Rigaku Miniflex IIdiffractometer. This diffractometer used Cu target X-ray. The operatingvoltage and current were 30 KV and 15 mA, respectively. The scanningspeed was 5 degrees/min. The scanning range was 5-65 degree. Thesimulated pattern of the powder diffraction is obtained by mercurysoftware based on the single crystal structure of monoclinic Ga₂S₃.Infrared transmission spectrum was obtained using Spectrum One Fouriertransform infrared spectrograph manufactured by Perkin-Elmer. Thetesting range was 4000-400 cm⁻¹. The sample powder and KBr wassufficiently grinded at a ratio of 1:100 and pressed for testing. Therewas no obvious adsorption peak in the range of 4000-400 cm⁻¹.

An ultraviolet diffuse reflectance spectrum was measured using Lambda900 UV-vis-near infrared spectrograph manufactured by Perkin-Elmer. Anintegrating sphere was employed. The testing range was 190-2500 nm. ABaSO₄ plate was used as reference. Sufficiently grinded sample powderwas placed thereon. The absorption spectrum is calculated from diffusereflectance spectrum using Kubelka-Munk formula α/S=(1−R)²/2R (R is thereflectivity, S is the scattering coefficient, α is the absorptioncoefficient).

As shown by FIGS. 1, 2, and 3, there was no impure peak in powderdiffraction pattern, indicating a high purity of the compound preparedby the high temperature solid-state boron-sulfur method. Infraredtransmission spectrum showed that the compound was infrared transparentin the range of 2.5-25 μm. UV-vis diffuse reflectance spectrum showedthat the energy gap of the compound was about 2.80 eV.

Example 5 SHG Phase Matching Test of the Monoclinic Ga₂S₃ Powder

The monoclinic Ga₂S₃ polycrystalline powder was sieved with a steelsieve, and divided into six powder samples having particle size rangesof 30-50, 50-75, 75-100, 100-150, 150-200, and 200-300 μm, respectively.The samples were charged and placed on the light path of the laser. Theintensities of SHG signals thereof at an infrared laser wavelength of1910 nm were measured with a near infrared CCD. The phase matchingbehavior of the compound was judged after a diagram was made. Thetesting results of the powder SHG phase matching were shown in FIG. 4.

As shown by FIG. 4, the second order nonlinear optical effect testshowed that, this compound had a relatively large second order nonlinearoptical effect. The SHG signals of the sample increased as the particlesize thereof increased. The intensities of SHG signal were about 0.7times of that of KTP, and the monoclinic Ga₂S₃ phase matched under 1910nm laser. It may be used as a nonlinear optical crystal material.

Example 6 Laser Damage Threshold Test of Monoclinic Phase Ga₂S₃

The monoclinic phase Ga₂S₃ polycrystalline powder was sieved as thepowder sample having a particle size range of 50-75 μm with a steelsieve. After the sample was charged, the laser damage threshold thereofwas measured under a laser at 1064 nm having a pulse width of about 8ns. The powder of the laser was continuously increased, and the damagesituation of the sample was observed, until damage spot occurred on thesample. The laser power at this time was recorded, and the main damagespot area was measured as 2.45 mm².

The laser damage threshold test of polycrystalline powder sample showedthat, the laser damage threshold of this compound was 174 MW/cm², whichwas larger than that of classical infrared nonlinear crystal AGS (0.03GW/cm²@1064 nm with τ_(p) as 10 ns) and LIS (0.1 GW/cm²@1064 nm withτ_(p) as 10 ns).

Example 7

The crystal obtained in Example 3 was subjected to directionally cuttingand polishing treatment, to make an optical parametric device. AQ-switched Nd:YAG laser light source having wavelength of 1.064 μm wasused as the pump light source, to produce a laser output of 3-14micrometers.

Example 8

The crystal obtained in Example 3 was subjected to directionally cuttingand polishing treatment, to make an optical parametric device. AQ-switched Nd:YAG laser light source having wavelength of 1.34 μm wasused as the pump source, to produce a laser output of 3-14 micrometers.

Example 9

The crystal obtained in Example 3 was subjected to directionally cuttingand polishing treatment, to make an optical parametric device. AQ-switched Ho:YAG laser light source having wavelength of 2.06 μm wasused as the pump source, to produce a laser output of 3-14 micrometers.

Example 10 The Performance Test of the Second Harmonic Generator

A second harmonic generator was produced using the monoclinic Ga₂S₃crystal produced in Example 3 as the nonlinear optical frequencyconversion crystal, and a pump laser source. It was observed via outputprofile test that, this second harmonic generator may still produce goodoutput profile at high output.

Example 11 The Performance Test of the Optical Parametric Oscillator

An optical parametric oscillator was produced using the monoclinic Ga₂S₃crystal prepared in Example 3 as a nonlinear optical frequencyconversion crystal, a first lens, a laser crystal, and a second lens. Itwas observed via output profile test that, this optical parametricoscillator may still produce good output profile at high output.

The invention claimed is:
 1. A second harmonic generator, comprising:one or more nonlinear optical frequency conversion crystals and a pumplaser source, wherein the one or more nonlinear optical frequencyconversion crystals are monoclinic Ga₂S₃ crystals, the space group ofthe monoclinic Ga₂S₃ crystal is Cc, and the unit cell parameters area=11.1 Å, b=6.4 Å, c=7.0 Å, α=90°, β=121°, γ=90°, and Z=4.
 2. The secondharmonic generator according to claim 1, wherein the wavelength of thelaser emitted by the pump laser source is between 1 to 20 micrometers.3. The second harmonic generator according to claim 1, wherein the pumplaser source is a liquid laser, a solid laser, a gas laser or asemiconductor laser.
 4. The second harmonic generator according to claim1, wherein the pump laser source is a continuous wave laser or a pulselaser.
 5. The second harmonic generator according to claim 1, whereinmanners for achieving phase matching in the nonlinear optical crystal bythe pump laser source comprise collinear, non-collinear, critical andnon-critical phase matching.
 6. The second harmonic generator accordingto claim 1, wherein the area of the monoclinic Ga₂S₃ crystal is from 0.5to 5 cm².
 7. The second harmonic generator according to claim 1, whereinthe area of the monoclinic Ga₂S₃ crystal is from 1.0 to 5 cm².
 8. Thesecond harmonic generator according to claim 1, wherein the area of themonoclinic Ga₂S₃ crystal is from 1.5 to 5 cm².
 9. The second harmonicgenerator according to claim 1, wherein the area of the monoclinic Ga₂S₃crystal is from 2.0 to 5 cm².
 10. The second harmonic generatoraccording to claim 1, wherein the area of the monoclinic Ga₂S₃ crystalis from 2.5 to 5 cm².
 11. The second harmonic generator according toclaim 1, wherein the area of the monoclinic Ga₂S₃ crystal is from 3.0 to5 cm².
 12. The second harmonic generator according to claim 1, whereinthe area of the monoclinic Ga₂S₃ crystal is from 3.5 to 5 cm².
 13. Thesecond harmonic generator according to claim 1, wherein the area of themonoclinic Ga₂S₃ crystal is from 5 to 10 cm².
 14. The second harmonicgenerator according to claim 1, wherein the output power of the secondharmonic generator is 0.5 W or more.